A circle's center is at $(2 ,5 )$ and it passes through $(1 ,4 )$ . What is the length of an arc covering $( pi ) /3$ radians on the circle?

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Answer 1 · 2016-02-17T03:59:01

length of arc $=(sqrt2*pi)/3=1.48096" "$ units

To solve for the length of arc s:
Use the formula

$s=r*theta$ using the given data: $theta=pi/3$ and computed value of $r$

to compute for r: use distance formula with points center $(x_c, y_c)=(2, 5)$ and the given point $(x_1, y_1)=(1, 4)$

$r=sqrt((x_c-x_1)^2+(y_c-y_1)^2)$

$r=sqrt((2-1)^2+(5-4)^2)$

$r=sqrt2$

Solve arc length $s$

$s=r*theta=sqrt2 *pi/3$

$s=(sqrt2*pi)/3=1.48096" "$ units

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A circle's center is at (2 ,5 )(2 ,5 ) and it passes through (1 ,4 )(1 ,4 ). What is the length of an arc covering ( pi ) /3 ( pi ) /3 radians on the circle?